14/5y=50-4y

Solution for 14/5y=50-4y equation:

14/5y=50-4y

We move all terms to the left:

14/5y-(50-4y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

14/5y-(-4y+50)=0

We get rid of parentheses

14/5y+4y-50=0

We multiply all the terms by the denominator


4y*5y-50*5y+14=0

Wy multiply elements

20y^2-250y+14=0

a = 20; b = -250; c = +14;
Δ = b2-4ac
Δ = -2502-4·20·14
Δ = 61380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{61380}=\sqrt{36*1705}=\sqrt{36}*\sqrt{1705}=6\sqrt{1705}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-6\sqrt{1705}}{2*20}=\frac{250-6\sqrt{1705}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+6\sqrt{1705}}{2*20}=\frac{250+6\sqrt{1705}}{40}
$